The present invention relates to the art of diagnostic imaging. It finds particular application in conjunction with single photon emission computed tomography (SPECT) scanners with cone-beam collimation for medical diagnostic imaging and will be described with particular reference thereto. It is to be appreciated, however, that the invention will have other applications in which cone-beam type data is reconstructed into an image representation for medical, quality assurance, and other examinations. Although described in conjunction with emission radiation sources which emit radiation from the subject, it will be appreciated that the present invention is also applicable to reconstructing image representation from transmission radiation sources which transmit radiation through a subject.
Cone-beam collimators are commonly used with single photon emission computed tomography and other gamma camera devices. The cone-beam collimator diverges outward from a subject toward the scintillation crystal or detector head. This enables a large fraction of the detector head crystal face to be utilized when imaging relatively small regions of the patient, e.g. the heart. This effective magnification produces a combination of resolution and sensitivity gains over images formed using parallel or fan beam collimators.
Most commonly, cone-beam projection data is converted into image representations using a technique developed by Feldkamp, Davis, and Kress which is described in "Practical Cone-Beam Algorithm", J. Opt. Soc. Am. Vol. I, pp. 612-619 (1984). The Feldkamp technique uses an algorithm which was derived using approximations of a fan beam formula. A fan beam commonly lies in a single plane, but diverge in that plane. When multiple fan beams are used concurrently, the planes are substantially parallel. In this manner, the radiation paths diverge along one axis and are parallel in the other axis of the plane of reception.
Feldkamp, et al. use a convolution and backprojection method which assumes that the focal point orbit is a circle. However, if the focal point of the collimator follows a single, planar orbit, the obtained data is not sufficient for an exact three-dimensional reconstruction. The insufficiency in the amount of collected data causes distortions and artifacts in the resultant image. There are three kinds of artifacts in the images reconstructed by the Feldkamp, et al. algorithm: a) reduced activity on non-central slices; b) cross-talk between non-central adjacent slices; and, c) undershoots in the transverse direction.
In order to generate a complete or sufficient set of data, every plane which passes through the imaging field of view must also cut through the orbit of the focal point at least once. See Tuy "An Inversion Formula for Cone-Beam Reconstruction", SIAM J. Appl. Math. Vol. 43, pp. 546-552 (1983). The single planar orbit of Feldkamp does not satisfy this condition.
Once the projection data complete, one reconstruction approach is to convert the cone-beam projections to Radon transforms and use the Radon inversion formula to reconstruct the image. This technique involves rebinning or sorting of the cone-beam data into another format. See Grangeat "Analysis d'un Systeme D'Imagerie 3D par Reconstruction a Partir De X en Geometrie Conique" Ph.D. Thesis 1'Ecole Nationale Superieure Des Telecommunications (1987).
Others have proposed mathematical improvements to the reconstruction algorithms. For example, the cone-beam data sets can be inverted if one assumes that for any line that contains a vertex point and a reconstruction point, there is an integer M (which remains constant for the line) such that almost every plane that contains this line intersects the geometry exactly M times. See Smith "Cone-Beam Tomography: Recent Advances and a Tutorial Review", Optical Engineering, Vol. 29 (5), pp 524-534 (1990). However, this integer requirement condition is too restrictive for practical application.
The present invention provides an exact reconstruction algorithm for reconstructing data from a helical orbit, which satisfies the sufficiency condition and overcomes the above-referenced problems.